A group of Mathematics faculty at the local college consists of 6 women and 9 men. Five people are to be selected to go to a conference. How many different ways can a group of five people be selected from this group of 15? In how many ways can five women be chosen from the group of 6 women?

What is the probability that all women will be chosen to attend the conference? Enter a reduced fraction or decimal.

Me asap on # : explain how factoring a trinomial, ax^2+ bx+ c, when a does not equal 1 different from factoring a trinomial when a = 1.

It is saturday morning and jeremy has discovered he has a leak coming from the water heater in his attic. since plumbers charge extra to come out on the weekends, jeremy is planning to use buckets to catch the dripping water. he places a bucket under the drip and steps outside to walk the dog. in half an hour the bucket is 1/5 of the way full. what is the rate at which the water is leaking per hour?

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)